There are many kinds of audio equipment that show a non-linear behavior and then inherently are difficult to simulate. Microphones, pre-amplifiers, power-amplifiers and loud speaker cabinets are some examples of non-linear audio equipment. Of particular importance are the old-fashioned amplifiers used by for instance guitarists, that contain electronic vacuum tubes. Professional and amateur guitar players appreciate the sound of classic tube amplifiers. The warm sound of their dynamic distortion has turned out to be quite hard to mimic with transistor based amplifiers. In addition to a small second hand market of original amplifiers, so called re-issues are available commercially. The main drawbacks with these ones are: high price, high cost for spare parts (transformers, tubes, capacitors etc), large manufacturing variations between the tubes, high power consumption and the sometimes unpleasant fact that one has to use a high output level to get saturation and the required distortion. Another inherent drawback is that guitar players want to shift between different amplifiers and special effects, which require several cable re-connections or additional switching hardware, and a lot of expensive and space-requiring hardware.
Therefore, several products exist today for simulating the tube distortion in analog electronics, or using software solutions in digital signal processors. Examples of this kind of technology are found in UK Patent GB 2.040.632 (H. Peavey, Sound amplifiers, August 1980, Peavey), U.S. Pat. No. 5,789,689 (M. Doidic, M. Mecca, M. Ryle, and C. Senffner, Tube modeling programmable digital guitar amplification system, August 1998, Line 6) and U.S. Pat. No. 6,350,943 (K. Matsumoto, M. Suruga, and Y. Suzuki, Electric instrument amplifier, February 2002, Korg). The point is that the products become cheaper, smaller in size and much more flexible in that the user can switch between different amplifiers, pre-amps, loudspeaker models and additional effects (delay, echo, chorus, reverbation, equalizer, auto-volume and so on). However, when switching between these prior attempts of tube emulating systems and one of the original amplifiers they are said to mimic, musicians and even amateurs can hear the difference.
The task of modeling and simulating a dynamic system is a well-established area in engineering. This area is described in e.g. the text book L. Ljung and T. Glad, Modeling of dynamic systems (Prentice-Hall, 1996), where it is pointed out that there is no principal difference between modeling and simulation of economic and biologic systems, paper plants and electric systems. A dynamic system can be any physical or abstract process where one can observe its input and the outputs the process produces. Audio equipment and in particular a tube amplifier fits very well in this framework and is no exception to this general problem. The most critical problem is to find a good model of the dynamical system at hand, and if no physical model can be made, as is the case for the complicated nature of a tube amplifier, one should aim at estimating a model that fits observed input-output data from the system. This task is called system identification, and it is also a quite well established research area with long traditions for identifying models of dynamic systems, see the text books L. Ljung, System identification, Theory for the user (Prentice Hall, Englewood Cliffs, N.J., second edition, 1999), and T. Söderström and P. Stoica, System identification (Prentice Hall, N.Y., 1989) for instance, and the commercial software packages System Identification Toolbox for Matlab (The MathWorks, Inc, Natick, Mass., 1999) and Frequency Identification Toolbox for Matlab (The MathWorks, Inc, Natick, Mass., 1995). The general approach is as follows: Design an experiment and collect data from the dynamical system, here the guitar input and the output from the amplifier, for example the loudspeaker signal. ‘Guess’ a model structure (linear or non-linear discrete time filter, or a combination thereof). Use a numerical algorithm to adjust the free parameters in the model structure such that the discrepancy between the measured signals and model predictions are minimized. For linear systems, there is a variety of model structures and software tools to choose among. The theory of modeling linear dynamics is well-known and found in any text book in signal processing or modeling L. Ljung and T. Glad, Modeling of dynamic systems and J. G. Proakis and D. G. Manolakis, Digital signal processing—principles, algorithms and applications (Prentice-Hall International, New Jersey, 3 edition, 1996).
For non-linear systems, for instance tube amplifiers, certain series connections of linear black box models with static non-linearities (SNL) (a so called Wiener model) have been suggested, see L. Ljung, System identification, Theory for the user and D. Atherton Nonlinear Control Engineering. This is also what has been used in previous art, such as U.S. Pat. No. 5,789,689. A typical engineer in the system identification community would try several such structures, use standard software to identify free parameters in each structure from observed input-output data, and probably in the end find a fair approximation but conclude that no known standard structure is perfectly suitable for high-performance tube amplifiers. In prior art there is therefore a lack of satisfying models for simulating tube amplifiers in a natural sounding manner. Our findings is that standardized model structures consisting of series connection of linear dynamics and static non-linearities (SNL's) cannot model the complicated behavior of for instance tubes.
Audio equipment that can be controlled by potentiometers can be simulated in software by using a number of fixed filters, and then interpolating between these. A piece of prior art is the U.S. Pat. No. 6,222,110, which describes a method for interpolating two second order filters.